powdR (version 1.1.0)

fps.powdRlib: Full pattern summation

Description

fps.powdRlib returns estimates of phase concentrations using full pattern summation of X-ray powder diffraction data.

Usage

# S3 method for powdRlib
fps(
  lib,
  smpl,
  harmonise,
  solver,
  obj,
  refs,
  std,
  std_conc,
  tth_align,
  align,
  manual_align,
  tth_fps,
  shift,
  shift_res,
  remove_trace,
  ...
)

Arguments

lib

A powdRlib object representing the reference library. Created using the powdRlib constructor function.

smpl

A data frame. First column is 2theta, second column is counts

harmonise

logical parameter defining whether to harmonise the lib and smpl. Default = TRUE. Harmonises to the intersecting 2theta range at the coarsest resolution available.

solver

The optimisation routine to be used. One of c("BFGS", "Nelder-Mead", "CG", "L-BFGS-B", or "NNLS"). Default = "BFGS".

obj

The objective function to minimise when "BFGS", "Nelder-Mead", "CG" or "L-BFGS-B" are used as the `solver` argument. One of c("Delta", "R", "Rwp"). Default = "Rwp". See Chipera and Bish (2002) and page 247 of Bish and Post (1989) for definitions of these functions.

refs

A character string of reference pattern ID's or names from the specified library. The ID's or names supplied must be present within the lib$phases$phase_id or lib$phases$phase_name columns.

std

The phase ID (e.g. "QUA.1") to be used as internal standard. Must match an ID provided in the phases parameter.

std_conc

The concentration of the internal standard (if known) in weight percent. If unknown then use std_conc = NA, in which case it will be assumed that all phases sum to 100 percent (default).

tth_align

A vector defining the minimum and maximum 2theta values to be used during alignment. If not defined, then the full range is used.

align

The maximum shift that is allowed during initial 2theta alignment (degrees). Default = 0.1.

manual_align

A logical operator denoting whether to optimise the alignment within the negative/position 2theta range defined in the align argument, or to use the specified value of the align argument for alignment of the sample to the standards. Default = FALSE, i.e. alignment is optimised.

tth_fps

A vector defining the minimum and maximum 2theta values to be used during full pattern summation. If not defined, then the full range is used.

shift

The maximum shift (degrees 2theta) that is allowed during the grid search phases selected from the non-negative least squares. Default = 0).

shift_res

A single integer defining the increase in resolution used during grid search shifting. Higher values facilitate finer shifts at the expense of longer computation. Default = 4.

remove_trace

A single numeric value representing the limit for the concentration of trace phases to be retained, i.e. any mineral with an estimated concentration below `remove_trace` will be omitted. Default = 0.

...

other arguments

Value

a list with components:

tth

a vector of the 2theta scale of the fitted data

fitted

a vector of the fitted XRPD pattern

measured

a vector of the original XRPD measurement (aligned)

residuals

a vector of the residuals (fitted vs measured)

phases

a dataframe of the phases used to produce the fitted pattern

phases_grouped

the phases dataframe grouped by phase_name and summed

rwp

the Rwp of the fitted vs measured pattern

weighted_pure_patterns

a dataframe of reference patterns used to produce the fitted pattern. All patterns have been weighted according to the coefficients used in the fit

coefficients

a named vector of coefficients used to produce the fitted pattern

inputs

a list of input arguments used in the function call

Details

Applies full pattern summation (Chipera & Bish, 2002, 2013; Eberl, 2003) to an XRPD sample to quantify phase concentrations. Requires a powdRlib library of reference patterns with reference intensity ratios in order to derive mineral concentrations.

References

Bish, D.L., Post, J.E., 1989. Modern powder diffraction. Mineralogical Society of America.

Chipera, S.J., Bish, D.L., 2013. Fitting Full X-Ray Diffraction Patterns for Quantitative Analysis: A Method for Readily Quantifying Crystalline and Disordered Phases. Adv. Mater. Phys. Chem. 03, 47-53. doi:10.4236/ampc.2013.31A007

Chipera, S.J., Bish, D.L., 2002. FULLPAT: A full-pattern quantitative analysis program for X-ray powder diffraction using measured and calculated patterns. J. Appl. Crystallogr. 35, 744-749. doi:10.1107/S0021889802017405

Eberl, D.D., 2003. User's guide to RockJock - A program for determining quantitative mineralogy from powder X-ray diffraction data. Boulder, CA.

Examples

# NOT RUN {
#Load the minerals library
data(minerals)

# Load the soils data
data(soils)

#Since the reference library is relatively small,
#the whole library can be used at once to get an
#estimate of the phases within each sample.
# }
# NOT RUN {
fps_sand <-  fps(lib = minerals,
                 smpl = soils$sandstone,
                 refs = minerals$phases$phase_id,
                 std = "QUA.1",
                 align = 0.2)

fps_lime <- fps(lib = minerals,
                smpl = soils$limestone,
                refs = minerals$phases$phase_id,
                std = "QUA.1",
                align = 0.2)

fps_granite <- fps(lib = minerals,
                   smpl = soils$granite,
                   refs = minerals$phases$phase_id,
                   std = "QUA.1",
                   align = 0.2)

#Alternatively run all 3 at once using lapply

fps_soils <- lapply(soils, fps,
                    lib = minerals,
                    std = "QUA.2",
                    refs = minerals$phases$phase_id,
                    align = 0.2)

#Using the rockjock library:

data(rockjock)
data(rockjock_mixtures)

rockjock_1 <- fps(lib = rockjock,
                  smpl = rockjock_mixtures$Mix1,
                  refs = c("ORDERED_MICROCLINE",
                           "LABRADORITE",
                           "KAOLINITE_DRY_BRANCH",
                           "MONTMORILLONITE_WYO",
                           "ILLITE_1M_RM30",
                           "CORUNDUM"),
                  std = "CORUNDUM",
                  align = 0.3)

#Alternatively you can specify the internal standard
#concentration if known:
rockjock_1s <- fps(lib = rockjock,
                 smpl = rockjock_mixtures$Mix1,
                 refs = c("ORDERED_MICROCLINE",
                          "LABRADORITE",
                          "KAOLINITE_DRY_BRANCH",
                          "MONTMORILLONITE_WYO",
                          "ILLITE_1M_RM30",
                          "CORUNDUM"),
                 std = "CORUNDUM",
                 std_conc = 20,
                 align = 0.3)

# }